已知函数f(x)=-1+2根号3sinxcosx+2cos2x.
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已知函数f(x)=-1+2根号3sinxcosx+2cos2x.
1·求f(x)的单调区间;2·若角α,β的终边不共线,且f(α)=f
(β),求tan(α+β)的值.
1·求f(x)的单调区间;2·若角α,β的终边不共线,且f(α)=f
(β),求tan(α+β)的值.
![已知函数f(x)=-1+2根号3sinxcosx+2cos2x.](/uploads/image/z/17137481-41-1.jpg?t=%E5%B7%B2%E7%9F%A5%E5%87%BD%E6%95%B0f%EF%BC%88x%EF%BC%89%3D-1%2B2%E6%A0%B9%E5%8F%B73sinxcosx%2B2cos2x.)
f(x)=-1+2根号3sinxcosx+2cos2x
=√3sin2x+cos2x
=2sin(2x+π/6)
1.单增区间为2x+π/6∈[2kπ-π/2,2kπ+π/2] x∈[kπ-π/3,kπ+π/6]
单减区间为2x+π/6∈[2kπ+π/2,2kπ+3π/2] x∈[kπ+π/6,kπ+2π/3]
2.若角α,β的终边不共线,且f(α)=f(β)
则α,β之间相差π
即α+β=2kπ+π
所以tan(α+β)=tan(2kπ+π)=tanπ=0
=√3sin2x+cos2x
=2sin(2x+π/6)
1.单增区间为2x+π/6∈[2kπ-π/2,2kπ+π/2] x∈[kπ-π/3,kπ+π/6]
单减区间为2x+π/6∈[2kπ+π/2,2kπ+3π/2] x∈[kπ+π/6,kπ+2π/3]
2.若角α,β的终边不共线,且f(α)=f(β)
则α,β之间相差π
即α+β=2kπ+π
所以tan(α+β)=tan(2kπ+π)=tanπ=0
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